Approximating High-Dimensional Dynamic Models: Sieve Value Function Iteration
Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the: (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the model's parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.
Arcidiacono, Bayer, and Bugni thank the National Science Foundation for research support via grant SES-1124193. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
"Approximating High Dimensional Dynamic Models: Sieve Value Function Iteration" with Pat Bayer, Federico Bugni, and Jon James, Advances in Econometrics, Vol. 31 (December 2013), 45-96.